I finished the research into the question of whether my Singer 3400 XL or my Bernina 1530 will do twin needle stitching and the answer is, yes. They both do this stitching. The both have a general purpose needle plate so the opening is wide enough for the twin needle and they both have presser feet that accommodate the twin needle. The only thing I will have to fiddle with is that the Singer only has one spool pin (the Bernina has two), so I will have to place a spool on the lone spool pin and one on my thread holder. I did some practice stitching. The blue stitching is the Bernina and the red stitching is the Singer. I will make a note of these findings in the owner's manuals along with notations about the feet, needle plate, stitch length setting, and spool pins.
I started the stitching at the normal 2.0 setting but the stitching came out much nicer at a longer length setting, I think I ended up at 3.0 or 3.5.